Problem on group theory cardinality and isomorphism

Question

Assignment:

Group Theory:

a. If S and T are sets then let T^S denote the set of all functions from S to T.  Prove that the cardinality of T^SxU equals the cardinality of (T^S)^U

b. Consider the groups Z₃ x Z₃ and Z₉.  These are each "integer groups" of order 9.  Are they isomorphic or not? Give an explicit reason.

Z- integer

Provide complete and step by step solution for the question and show calculations and use formulas.